Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators

Lu, Weijie; Pinto, Manuel; Xia, Yonghui

doi:10.1098/rspa.2021.0957

Cited by 4 publications

(1 citation statement)

References 48 publications

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“…Additionally, we modeled the seasonal births through a succession of discrete times, which generates a discontinuity in the abundance curves, differentiating the demographic patterns of each species. This system of differential equations is known as an impulsive system and provides a theoretical framework that captures this phenomenon (Samoilenko and Perestyuk 1995;González and Pinto 1996;Hakl et al 2017;Pinto et al 2018;Castillo et al 2019;Lu et al 2022) 12where, the variation discrete is defined with . Products , and…”

Section: Model Formulationmentioning

confidence: 99%

Body size modulates demographic patterns of top predators and their native and invasive prey: A biomathematical approach

Campillay-Llanos,

Pinto,

Osorio

2024

Ecol Austral

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The arrival of invasive species in native communities impacts the structure and functioning of ecosystems, and is considered a critical indicator of loss of biodiversity. Exploring the effects of new species in communities presents challenges addressable through theoretical ecology. Species body size not only shapes trophic relationships, but may also impact predator success and facilitate species coexistence. However, little attention has been paid to the effects of differences in species body size on interactions between native and invasive primary consumers, which could be relevant to their coexistence with higher-level predators. Our aim is to investigate demographic patterns using a dynamic, mechanistic model of two age-structured primary consumers (one invasive and one native) sharing a plant resource and preyed upon by a common predator. In our model, we highlight three crucial phenomena: the structuring of primary consumers into adults and juveniles, reproduction occurring in discrete pulses, and the seasonal addition of new individuals to the population. Hence, the success of one species over the other relies on its reproductive capacity to incorporate individuals in each reproductive cycle. Our simulations reveal that abundance patterns are influenced by body size, suggesting that changes in predator body size could serve as key indicators of shifts in community structure.

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Section: Model Formulationmentioning

confidence: 99%

Body size modulates demographic patterns of top predators and their native and invasive prey: A biomathematical approach

Campillay-Llanos,

Pinto,

Osorio

2024

Ecol Austral

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On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses

Chen,

Jin,

Wang

et al. 2024

Math. Ann.

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Complex skin modes in non-Hermitian coupled laser arrays

et al. 2022

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From biological ecosystems to spin glasses, connectivity plays a crucial role in determining the function, dynamics, and resiliency of a network. In the realm of non-Hermitian physics, the possibility of complex and asymmetric exchange interactions ($$\left| {\kappa _{ij}} \right| \ne \left| {\kappa _{ji}} \right|$$ κ i j ≠ κ j i ) between a network of oscillators has been theoretically shown to lead to novel behaviors like delocalization, skin effect, and bulk-boundary correspondence. An archetypical lattice exhibiting the aforementioned properties is that proposed by Hatano and Nelson in a series of papers in late 1990s. While the ramifications of these theoretical works in optics have been recently pursued in synthetic dimensions, the Hatano–Nelson model has yet to be realized in real space. What makes the implementation of these lattices challenging is the difficulty in establishing the required asymmetric exchange interactions in optical platforms. In this work, by using active optical oscillators featuring non-Hermiticity and nonlinearity, we introduce an anisotropic exchange between the resonant elements in a lattice, an aspect that enables us to observe the non-Hermitian skin effect, phase locking, and near-field beam steering in a Hatano–Nelson laser array. Our work opens up new regimes of phase-locking in lasers while shedding light on the fundamental physics of non-Hermitian systems.

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Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators

Cited by 4 publications

References 48 publications

Body size modulates demographic patterns of top predators and their native and invasive prey: A biomathematical approach

Body size modulates demographic patterns of top predators and their native and invasive prey: A biomathematical approach

On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses

Complex skin modes in non-Hermitian coupled laser arrays

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